Apologies for the vague title; couldn't really think of a better way of putting it.

I have a function $F$ of two variables, $\rho\in[0,\infty)$ and $f\in[0,1]$, that I wish to create a plot over (e.g. with CountourPlot or DensityPlot). I can numerically generate the entire curve of $F$ over $f$ for a particular value of $\rho$ relatively cheaply, but I can't directly compute $F$ for individual values of $f$.

Is there an efficient way of taking such a curve and plotting it for a range of $\rho$ without Mathematica having to evaluate the function independently at every $(\rho,f)$?

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